PreprintarXiv licencearXiv
Kählerity of complete almost-Kähler gradient shrinking Ricci solitons
Abstract
In this paper, we prove that any complete, compact or noncompact, almost-Kähler gradient shrinking Ricci soliton is Kähler in arbitrary even dimension. Among other applications, combining our result with the classification of complete gradient shrinking Kähler-Ricci solitons in complex dimension two, we obtain a full classification of complete almost-Kähler gradient shrinking Ricci solitons in real dimension four.
Related
- Complete steady and shrinking gradient Yamabe solitons
- Shrinking Kähler-Ricci solitons on toric fano fibrations
- Rigidity of shrinking Ricci solitons with low-dimensional focal sets
- Uniqueness of the soliton vector field of a shrinking gradient Kähler-Ricci soliton
- Ricci Solitons, Almost Theta-Yamabe Solitons, and Finite-Order Tensor Symmetries of a Vector Field on Riemannian Manifolds with Rank-One Anisotropic Curvature
BibTeX
@misc{xie2026kählerity,
title = {{Kählerity of complete almost-Kähler gradient shrinking Ricci solitons}},
author = {Junming Xie},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00840},
eprint = {2609.00840},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00840},
}
RIS
TY - UNPB
TI - Kählerity of complete almost-Kähler gradient shrinking Ricci solitons
AU - Junming Xie
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.00840
UR - https://arxiv.org/abs/2609.00840
AB - In this paper, we prove that any complete, compact or noncompact, almost-Kähler gradient shrinking Ricci soliton is Kähler in arbitrary even dimension. Among other applications, combining our result with the classification of complete gradient shrinking Kähler-Ricci solitons in complex dimension two, we obtain a full classification of complete almost-Kähler gradient shrinking Ricci solitons in real dimension four.
ER -